How do you use Heron's formula to find the area of a triangle with sides of lengths #9 #, #5 #, and #8 #?

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Answer 1 · 2016-02-02T00:50:38

#A=19.9# rounded to one decimal place

Heron's formula is #A=sqrt(s(s-a)(s-b)(s-c))#, where #s# is the semiperimeter of the triangle, which is half of its perimeter.

Let #a=9#, #b=5#, and #c=8#.

#s=(9+5+8)/2#

#s=22/2#

#s=11#

Substitute the known values into Heron's formula.

#A=sqrt(s(s-a)(s-b)(s-c))#

#A=sqrt(11(11-9)(11-5)(11-8))#

Simplify.

#A=sqrt(11(2)(6)(3))#

Simplify.

#A=sqrt(396)#

#A=19.9# rounded to one decimal place